Statistics and Probability Answers

If an automobile gets an average of 27 miles per gallon on a trip and the standard deviation is 3 miles per gallon, find the probability that on a randomly selected trip, the automobile will get between 21 and 30 miles per gallon. Assume the variable is normally distributed.

A lottery that pays off P300 000 000 is made available for 10 000 000 tickets. Each ticket costs P50. Suppose the variable Z gives the net winnings from playing the lottery. What is the expected gain for joining the lottery with only one ticket?

An employee is selected from a staff of 10 to supervise a certain project by selecting a tag at random from a box containing 10 tags numbered from 1 to 10. Find the formula for the probability distribution of X representing the number on the tag that is drawn.

Find the mean and variance of the random variable X

Grades assigned by an economics lecturer for his postgraduate coursework students at a SLIIT have historically followed a symmetrical distribution: 5% HDs, 25% Ds, 40% Cs, 25% Ps and 5% Fs. This year, a sample of grades revealed 11 HDs, 32 Ds, 62 Cs, 29 Ps and 16 Fs. Can you conclude, at the 1% level of significance, that this year’s marks are distributed differently from marks in the past?

A well-known consulting firm wants to test how it can influence the proportion of questionnaires returns for its surveys. In the belief that the inclusion of an inducement to respond may be influential, the firm sends out 1000 questioners: 200 promise to send respondents a summary of the survey results; 300 indicate that 20 respondents (selected by a lottery) will be awarded gifts; and 500 are accompanied by no inducements. Of these, 80 questionnaires promising a summary, 100 questionnaires offering gifts, and 120 questionnaires offering no inducements are returned. What can you conclude from these results?

each of the following situations, identify the population and the 

sample

 (i). There are 50 books in statistics in our library which contains a 

collection of 5,000 books

each of the following situations, identify the population and the 

sample

 (i). There are 50 books in statistics in our library which contains a 

collection of 5,000 books

a toy manufacturer uses this acceptance sampling plan: Randomly select and test 47 batteries and determine what batteries do not meet specifications. A shipment contains 4000 batteries, and 1% of them do not meet specifications. What is the prob be accepted , or will many be rejected?

BINOMDIST(2,52,0.02,TRUE)

In each of the following situations, identify the population and the sample

(i). There are 50 books in statistics in our library which contains a collection of 5,000 books.

(ii). About 20% of the stones heaped on the building site are round in shape.

(iii). The dream that there will be more female than male politicians in Ghana will never be realized

(iv) About 10% of pregnant mothers reporting to hospitals are infected with HIV virus.

(v) Since the last major earthquake in 1939, there have been 60 earth tremors in Ghana, with 20 these occurring over the past 5 years.